https://web.stanford.edu/~chadj/Consumption2009-11-25.pdf

Q1)

For this question assume that inflation is zero.

Consider a 2-period economy.

Assume that consumer's lifetime utility is given by

= log ₁ + 0.8 log ₂ (1)

Assume that the consumer starts period 1 with the initial wealth of 50,000.

The consumer gets labour income in period t (t=1,2).

₁ = 20,000, ₂ = 120,000, ₁ = 5,000, ₂ = 31,500 and R=0.05 (2)

Initially assume that there are no borrowing constraints.

a. Write down the Euler equation (with all values substituted) and explain its meaning. Write the intertemporal budget constraint and explain its meaning.

b. Solve consumer's problem of maximizing lifetime utility subject to the intertemporal budget constraint. Is the present value of consumption in the first and the second periods the same? Explain why.

c. If for some reason the consumer were facing the borrowing constraint, would it be binding? Explain.

d. Answer part a to part c for the case when =0.95 instead of 0.8 and R=0.5 instead of 0.05. (note that you don't have to repeat the explanation of the Euler equation and the intertemporal budget constraint.)